Advice on processing a color checker image

[felix-b1-jadehs]

Hi,
I'm currently working with a Raspberry Pi and a HQ camera module. I want to process the raw data from a dng-file to get values in the sRGB colorspace. For test puposes I tried to get the correct colors with a color checker but I'm a bit lost on the processing steps. My current progress is in a jupyter notebook here. I would be happy for any advice or information on how to get a better reconstruction of the real world colors.
I've completed this tutorial and tried to build my own white balance on what I've understood so far. I've selected a gray panel on the color checker and tried to match the theoretical target values for this specific panel. For this I've tried two different methods but neither of them produced sufficient results.

Edit 1: Link to notebook